Modeling changes in predator functional response to prey across spatial scales

Extrapolation of predator functional responses from laboratory observations to the field is often necessary to predict predation rates and predator-prey dynamics at spatial and temporal scales that are difficult to observe directly. We use a spatially explicit individual-based model to explore mechanisms behind changes in functional responses when the scale of observation is increased. Model parameters were estimated from a predator-prey system consisting of the predator Delphastus catalinae (Coleoptera: Coccinellidae) and Bemisia tabaci biotype B (Hemiptera: Aleyrodidae) on tomato plants. The model explicitly incorporates prey and predator distributions within single plants, the search behavior of predators within plants, and the functional response to prey at the smallest scale of interaction (within leaflets) observed in the laboratory. Validation revealed that the model is useful in scaling up from laboratory observations to predation in whole tomato plants of varying sizes. Comparing predicted predation at the leaflet scale, as observed in laboratory experiments, with predicted predation on whole plants revealed that the predator functional response switches from type II within leaflets to type III within whole plants. We found that the magnitude of predation rates and the type of functional response at the whole plant scale are modulated by (1) the degree of alignment between predator and prey distributions and (2) predator foraging behavior, particularly the effect of area-concentrated search within plants when prey population density is relatively low. The experimental and modeling techniques we present could be applied to other systems in which active predators prey upon sessile or slow-moving species.     

Parasitism-mediated prey selectivity in laboratory conditions and implications for biological control

In agroecosystems, parasitoids and predators may exert top-down regulation and predators for different reasons may avoid or give preference to parasitised prey, i.e., become an intraguild predator. The success of pest suppression with multiple natural enemies depends essentially on predator–prey dynamics and how this is affected by the interplay between predation and parasitism. We conducted a simple laboratory experiment to test whether predators distinguished parasitised prey from non-parasitised prey and to study how parasitism influenced predation. We used a host-parasitoid system, Spodoptera frugiperda and one of its generalist parasitoids, Campoletis flavicincta, and included two predators, the stinkbug Podisus nigrispinus and the earwig Euborellia annulipes. In the experiment, predators were offered a choice between non-parasitised and parasitised larvae. We observed how long it took for the predator to attack a larva, which prey was attacked first, and whether predators opted to consume the other prey after their initial attack. Our results suggest that, in general, female predators are less selective than males and predators are more likely to consume non-parasitised prey with this likelihood being directly proportional to the time taken until the first prey attack. We used statistical models to show that males opted to consume the other prey with a significantly higher probability if they attacked a parasitised larva first, while females did so with the same probability irrespective of which one they attacked first. These results highlight the importance of studies on predator–parasitoid interactions, as well as on coexistence mechanisms in agroecosystems. When parasitism mediates predator choice so that intraguild predation is avoided, natural enemy populations may be larger, thus increasing the probability of more successful biological control.     

Molecular gut-content analysis of a predator assemblage reveals the effect of habitat manipulation on biological control in the field

Habitat manipulation in agroecosystems can influence predator–prey interactions. In this study, we collected foliar predators from field potato plots with different mulch treatments and assayed them for DNA of the target prey, Leptinotarsa decemlineata (Say), using species-specific primers. Concurrently, L. decemlineata larval abundance and plant damage were recorded from the same plots. Predator species abundance and diversity were not influenced by habitat manipulation, while prey density was highest in plots without mulch. Gut-content analysis revealed that the highest incidence of predators positive for L. decemlineata DNA was in plots without mulch, where target prey abundance was highest. Therefore, the lower prey abundance in mulched plots was not due to predation. The most abundant species in the predator assemblage was Coleomegilla maculata, which had the lowest proportion of L. decemlineata DNA in the gut. Podisus maculiventris, Perillus bioculatus, and Lebia grandis were less abundant but had a higher incidence of target prey DNA in the gut. DNA detectability half-lives were used to adjust for inter-specific variation in DNA digestive rates of the four predator species. Using this information to adjust actual number of positives for prey DNA, we compared proportions positive for L. decemlineata and found that P. maculiventris is the most effective predator species in the complex.     

Bistability and limit cycles in generalist predator–prey dynamics

Since generalist predators feed on a variety of prey species they tend to persist in an ecosystem even if one particular prey species is absent. Predation by generalist predators is typically characterized by a sigmoidal functional response, so that predation pressure for a given prey species is small when the density of that prey is low. Many mathematical models have included a sigmoidal functional response into predator–prey equations and found the dynamics to be more stable than for a Holling type II functional response. However, almost none of these models considers alternative food sources for the generalist predator. In particular, in these models, the generalist predator goes extinct in the absence of the one focal prey. We model the dynamics of a generalist predator with a sigmoidal functional response on one dynamic prey and fixed alternative food source. We find that the system can exhibit up to six steady states, bistability, limit cycles and several global bifurcations.     

Functional responses modified by predator density

Realistic functional responses are required for accurate model predictions at the community level. However, controversy remains regarding which types of dependencies need to be included in functional response models. Several studies have shown an effect of very high predator densities on per capita predation rates, but it is unclear whether this predator dependence is also important at low predator densities. We fit integrated functional response models to predation data from 4-h experiments where we had varied both predator and prey densities. Using an information theoretic approach we show that the best-fit model includes moderate predator dependence, which was equally strong even at low predator densities. The best fits of Beddington–DeAngelis and Arditi–Akçakaya functional responses were closely followed by the fit of the Arditi–Ginzburg model. A Holling type III functional response did not describe the data well. In addition, independent behavioral observations revealed high encounter rates between predators. We quantified the number of encounters between predators and the time the focal predator spent interacting with other individuals per encounter. This time “wasted” on conspecifics reduced the total time available for foraging and may therefore account for lower predation rates at higher predator densities. Our findings imply that ecological theory needs to take realistic levels of predator dependence into account.     

Estimating predation rates in experimental systems: scale-dependent effects of aggregative behaviour

We studied the effect of arena size on estimates of prey mortality rate in predation experiments. In a laboratory experiment involving two of the dominating benthic species in the northern Baltic Sea, the predacious isopod Saduria entomon , and its main prey, the amphipod Monoporeia affinis , the prey mortality rate increased with container radius. The densities of both predator and prey close to the wall increased with container size. We hypothesised that this scale-dependent coaggregation of predator and prey caused the mortality rates to increase with arena size. We tested the hypothesis with the help of a simple model, by calculating the expected number of prey eaten in containers of different size from experimental data on the distributions of predator and prey within the arenas. A significant relationship between expected and observed numbers eaten supported our hypothesis. As the aggregative response was most pronounced in large arenas, this leads to the counterintuitive conclusion that large containers produced more biased estimates of morality rates than small containers.
To further study the effects of coaggregation we explored a general simulation model where both predator and prey preferred the habitat close to the arena wall. The model predicted a humpshaped relationship between encounter rate and arena size. This suggests that when predators and prey show a scale-dependent tendency to aggregate along arena walls, the most accurate estimates of predation rates may be obtained with very small or very large arenas.     

The Effects of Prey Patchiness, Predator Aggregation, and Mutual Interference on the Functional Response of Phytoseiulus persimilis Feeding on Tetranychus urticae (Acari: Phytoseiidae, Tetranychidae)

The spatial distributions of two-spotted spider mites Tetranychus urticae and their natural enemy, the phytoseiid predator Phytoseiulus persimilis, were studied on six full-grown cucumber plants. Both mite species were very patchily distributed and P. persimilis tended to aggregate on leaves with abundant prey. The effects of non-homogenous distributions and degree of spatial overlap between prey and predators on the per capita predation rate were studied by means of a stage-specific predation model that averages the predation rates over all the local populations inhabiting the individual leaves. The empirical predation rates were compared with predictions assuming random predator search and/or an even distribution of prey. The analysis clearly shows that the ability of the predators to search non-randomly increases their predation rate. On the other hand, the prey may gain if it adopts a more even distribution when its density is low and a more patchy distribution when density increases. Mutual interference between searching predators reduces the predation rate, but the effect is negligible. The stage-specific functional response model was compared with two simpler models without explicit stage structure. Both unstructured models yielded predictions that were quite similar to those of the stage-structured model.     

A functional response model of a predator population foraging in a patchy habitat

1. Functional response models (e.g. Holling's disc equation) that do not take the spatial distributions of prey and predators into account are likely to produce biased estimates of predation rates. 2. To investigate the consequences of ignoring prey distribution and predator aggregation, a general analytical model of a predator population occupying a patchy environment with a single species of prey is developed. 3. The model includes the density and the spatial distribution of the prey population, the aggregative response of the predators and their mutual interference. 4. The model provides explicit solutions to a number of scenarios that can be independently combined: the prey has an even, random or clumped distribution, and the predators show a convex, sigmoid, linear or no aggregative response. 5. The model is parameterized with data from an acarine predator-prey system consisting of Phytoseiulus persimis and Tetranychus urticae inhabiting greenhouse cucumbers. 6. The model fits empirical data quite well and much better than if prey and predators were assumed to be evenly distributed among patches, or if the predators were distributed independently of the prey. 7. The analyses show that if the predators do not show an aggregative response it will always be an advantage to the prey to adopt a patchy distribution. On the other hand, if the predators are capable of responding to the distribution of prey, then it will be an advantage to the prey to be evenly distributed when its density is low and switch to a more patchy distribution when its density increases. The effect of mutual interference is negligible unless predator density is very high. 8. The model shows that prey patchiness and predator aggregation in combination can change the functional response at the population level from type II to type III, indicating that these factors may contribute to stabilization of predator-prey dynamics.     

Searching behavior and time budgets of the predator Podisus maculiventris

Searching behavior of the predaceous insect Podisus maculiventris (Say) (Heteroptera: Pentatomidae) was investigated in the laboratory to verify assumptions made in a predator search model. Female predators were placed into an arena containing 30 lima bean plants (Phaseolus lunatus L.), each having five numbered leaflets. Prey were third-instar larvae of Mexican bean beetle (Epilachna varivestis Mulsant) at two densities. Predators were observed for 4 h periods as they searched the plant canopy. Results showed that predators searched a greater area and for longer at low prey density than at high prey density. Predators apparently searched plants without using cues, did not search areas of the canopy repeatedly after attacks, and spent approximately 1 h handling prey. Predators spent more time resting than searching, and attack rates were negatively correlated with rest time, but were not correlated with search time. Long resting periods by predators may be a result of energy conservation. The implications for using predators such as P. maculiventris against pests in crops are (i) the predators' searching behavior limits the number of prey attacked, and (ii) the predator may be able to persist at low prey densities better than species with different searching behaviors.     

Impacts of predation on dynamics of age-structured prey: Allee effects and multi-stability

With a series of mathematical models, we explore impacts of predation on a prey population structured into two age classes, juveniles and adults, assuming generalist, age-specific predators. Predation on any age class is either absent, or represented by types II or III functional responses, in various combinations. We look for Allee effects or more generally for multiple stable steady states in the prey population. One of our key findings is the occurrence of a predator pit (low-density ??refuge?? state of prey induced by predation; the chance of escaping predation thus increases both below and above an intermediate prey density) when only one age class is consumed and predators use a type II functional response ??this scenario is known to occur for an unstructured prey consumed via a type III functional response and can never occur for an unstructured prey consumed via a type II one. In the case where both age classes are consumed by type II generalist predators, an Allee effect occurs frequently, but some parameters give also rise to a predator pit and even three stable equilibria (one extinction equilibrium and two positive ones??Allee effect and predator pit combined). Multiple positive stable equilibria are common if one age class is consumed via a type II functional response and the other via a type III functional response??here, in addition to the behaviours mentioned above one may even observe three stable positive equilibria????double?? predator pit. Some of these results are discussed from the perspective of population management.     

Does aggregation benefit bark beetles by diluting predation? Links between a group‐colonisation strategy and the absence of emergent multiple predator effects

Abstract. 1. Aggregation in bark beetles (Coleoptera: Scolytidae) aids in mate attraction and resource procurement when colonising well‐defended plants; however, some species colonise primarily poorly defended plants, and intraspecific competition increases mortality. The hypothesis that decreased risk of predation was a potential benefit to aggregation in such circumstances was tested, using the pine engraver, Ips pini (Say) and its two major predators Thanasimus dubius (F.) (Coleoptera: Cleridae) and Platysoma cylindrica (Paykull) (Coleoptera: Histeridae). Both single‐ and multiple‐predator effects, across a range of prey densities, were tested. 2. Both male and female colonisation events increased with herbivore density, in an asymptotic fashion. 3. Predators decreased the number of colonisers in a density‐dependent manner, consistent with a type II functional response. 4. The proportional impact of predators decreased with increased herbivore colonisation densities. These findings indicate that predator dilution may be a viable benefit to aggregation. 5. Total emergence of the herbivore also increased with density, although the net replacement rate during one generation was independent of initial arrival density. This was likely due to larval predation, which negates potential relationships between per capita reproductive success and establishment density. 6. Each predator species decreased I. pini's net replacement rate by approximately 42%, and their combined effect was approximately 70%. 7. Overall, these predators modified their prey's establishment and adult mortality relationships in additive manners. This is somewhat surprising, given the potential for emergent effects due to interactions between multiple predators foraging within a common habitat. The persistence of additivity, rather than risk reduction or enhancement to the prey, may increase the predator‐swamping benefit to aggregation for this herbivore. 8. The effects of these predators are substitutable, and likely exert equivalent selective pressures to mask signals at the whole‐plant level.     

Prey: predator ratio dependence in the functional response of a freshwater amphipod

1. First known for their shredding activity, freshwater amphipods also behave as active predators with consequences for prey population regulation and amphipod coexistence in the context of biological invasions. 2. A way to quantify predation is to determine the average consumption rate per predator, also known as its functional response (FR). 3. Although amphipods are gregarious and can display social interactions that can alter per capita consumption rates, previous studies using the FR approach to investigate amphipod predation ignored such potential mutual interference because they did not consider variations in predator density. 4. We investigated the FR of Echinogammarus berilloni feeding on dipteran larvae with joint variations in prey and predator densities. This bivariate experimental design allowed us to estimate interference and to compare the fits of the three main classes of theoretical FR models, in which the predation rate is a function of prey density alone (prey‐dependent models), of both prey and predator densities (predator‐dependent models) or of the prey‐to‐predator ratio (ratio‐dependent models). 5. The Arditi–Ginzburg ratio‐dependent FR model provided the best representation of the FR of E. berilloni, whose predation rate showed a decelerating rise to a horizontal asymptote as prey abundance increased. 6. Ratio dependence means that mutual interference between amphipods leads to prey sharing. Mutual interference is likely to vary between amphipod species, depending on their level of aggressiveness.     

A predator's costs of overcoming the confusion-effect of swarming prey

Swarms of prey are known to have a confusion effect on predators that increases with swarm density. Hungry sticklebacks (Gasterosteus aculeatus) overcome the confusion (Heller & Milinski 1979) except when frightened by a predator of their own (Milinski & Heller 1978). This study investigates whether the costs of overcoming the confusion consist of decreased attention for predators. Hungry sticklebacks detected a predator of their own less often when they fed upon a prey swarm of high density than when they attacked a low density swarm. They also overlooked the predator more frequently when they fed with a high rate than with a low one in the same high density. Thus, there is a cost of attacking high density swarms. These results confirm two necessary conditions of a model for balancing feeding rate and predation risk (Milinski & Heller 1978). The decreased attention is assumed to be due to the limited channel capacity of the nervous system in processing sensory information.     

Flexible antipredator behaviour in herbivorous mites through vertical migration in a plant

When predation risk varies in space and time and with predator species, successful prey defence requires specific responses to each predator. In cassava fields in Africa, the herbivorous cassava green mite (Mononychellus tanajoa) is attacked by three predatory mite species that are segregated within the plant: the leaf-dwelling Typhlodromalus manihoti and Euseius fustis occur on the middle leaves, whereas the apex-inhabiting T. aripo migrates from the apex to the top leaves only during the night. We found that differential distributions of these predators allow prey to escape predation by vertical migration to other plant strata. We studied the role of odours in the underlying prey behaviour on predator-free plants placed downwind from plants with predators and prey or with prey only. Prey showed increased vertical migration in response to predator-related odours. Moreover, these responses were specific: when exposed to odours associated with T. manihoti, prey migrated upwards, irrespective of the plant stratum where they were placed. Odours associated with T. aripo triggered a flexible response: prey on the top leaves migrated downwards, whereas prey on the middle leaves migrated upwards. Odours associated with E. fustis, a low-risk predator, did not elicit vertical migration. Further experiments revealed that: (1) prey migrate up or down depending on the stratum where they are located, and (2) prey discrimination among predators is based upon the perception of predator species-specific body odours. Thus, at the scale of a single plant, odour-based enemy specification allows herbivorous mites to escape predation by vertical migration.     

Application of a model of scale dependence to quantify scale domains in open predation experiments

We use a model of open predation experiments to define scale domains that differ in terms of the controlling processes and scale dependence of predator impacts. For experimental arenas that are small compared to the movements of the prey (small scale domain) the model predicts that predator impacts are scale independent and controlled by prey movements. For arenas of intermediate scale we predict that predator impacts are scale dependent and controlled by both prey movements and direct predation, and for the largest scale domain we predict weak scale dependence and predation control.
We propose that the scale‐domain concept is useful when designing and interpreting field experiments. As an illustration we apply the concept to experiments examining predator effects on the stream benthos. First, we test two key assumptions of the underlying model: that area‐specific prey migration rates decrease with increasing size of experimental arenas and that predation rates are independent of arena size. For this purpose we used published estimates of prey emigration and predator consumption rates for nine studies examining the effects of stream predators on benthic prey. We found that prey per capita emigration rates but not predation rates decreased with increasing arena length.
Second, we demonstrate a method for identifying the scale domain of real experiments. The model of predation experiments was parameterized using experimental data and the expected spatial and temporal scale dependence of predator impacts on prey in these experiments was simulated. The simulations suggest that the studies conducted in the largest arenas (length 15–35 m) should be classified as large‐scale, consumption‐controlled experiments, whereas the experiments conducted in smaller arenas (length 1.5–6 m) should be classified as small or intermediate‐scale. We also attempted to determine the scale domain of the experiments in a large data set, including results from most published stream predation experiments. The majority of arenas used in these experiments (73%) were smaller than 1 m in length. Our data on the scale dependence of predation and prey migration rate suggest that experiments in this scale range (<1 m) should be classified as small‐scale, movement‐controlled experiments for most prey taxa.     

Predator interference alters foraging behavior of a generalist predatory arthropod

Interactions between predators foraging in the same patch may strongly influence patch use and functional response. In particular, there is continued interest in how the magnitude of mutual interference shapes predator–prey interactions. Studies commonly focus on either patch use or the functional response without attempting to link these important components of the foraging puzzle. Predictions from both theoretical frameworks suggest that predators should modify foraging efforts in response to changes in feeding rate, but this prediction has received little empirical attention. We study the linkage between patch departure rates and food consumption by the hunting spider, Pardosa milvina, using field enclosures in which prey and predator densities were manipulated. Additionally, the most appropriate functional response model was identified by fitting alternative functional response models to laboratory foraging data. Our results show that although prey availability was the most important determinant of patch departure rates, a greater proportion of predators left enclosures containing elevated predator abundance. Functional response parameter estimation revealed significant levels of interference among predators leading to lower feeding rates even when the area allocated for each predator was kept constant. These results suggest that feeding rates determine patch movement dynamics, where interference induces predators to search for foraging sites that balance the frequency of agonistic interactions with prey encounter rates.     

Effect of Prey and Predator Density on Predation of Rice Leaffolder Eggs by the Cricket Metioche vittaticollis

Cage experiments were conducted to quantify the predation rate of the cricket Metioche vittaticollis (Sta ˚l) on the eggs of rice leaffolder Marasmia patnalis Bradley. Egg predation by adult females was measured in response to changes in egg density, predator density and leaf area per cage. The number of eggs consumed per predator increased with egg density, without reaching a plateau. The predation rate decreased with increasing leaf area. The functional response could be adequately described with a linear Type I model, with the effect of leaf area included. This type of response to leaffolder egg density means that predation was not limited by prey handling time or satiation, but by the search rate. The search rate is here interpreted as the leaf area effectively searched for leaffolder eggs by a single predator in one day. Estimated search rates averaged 0.13 m 2 day -1 for M. vittaticollis females. The search rate of the predators increased with prey density, but a model describing a density dependent search rate explained only 3% of the total variation in search rate. Increasing predator density per cage led to a decrease in the per capita egg predation rate when predator density was more than two per m 2 leaf area. Interference might thus reduce the potential to enhance leaffolder egg predation by conservation or augmentation of predatory cricket populations.     

Two common invertebrate predators show varying predation responses to different types of sentinel prey

Sentinel prey (an artificially manipulated patch of prey) are widely used to assess the level of predation provided by natural enemies in agricultural systems. Whilst a number of different methodologies are currently in use, little is known about how arthropod predators respond to artificially manipulated sentinel prey in comparison with predation on free‐living prey populations. We assessed how attack rates on immobilized (aphids stuck to cards) and artificial (plasticine lepidopteran larvae mimics) sentinel prey differed to predation on free‐moving live prey (aphids). Predation was assessed in response to density of the common invertebrate predators, a foliar‐active ladybird Harmonia axyridis (Coleoptera: Coccinellidae), and a ground‐active beetle Pterostichus madidus (Coleoptera: Carabidae). Significant increases in attack rates were found for the immobilized and artificial prey between the low and high predator density treatments. However, an increased predator density did not significantly reduce numbers of free‐living live aphids included in the mesocosms in addition to the alternate prey. We also found no signs of predation on the artificial prey by the predator H. axyridis. These findings suggest that if our assessment of predation had been based solely on the foliar artificial prey, then no increase in predation would have been found in response to increased predator density. Our results demonstrate that predators differentially respond to sentinel prey items which could affect the level of predation recorded where target pest species are not being used.     

A spatial theory for characterizing predator–multiprey interactions in heterogeneous landscapes

Trophic interactions in multiprey systems can be largely determined by prey distributions. Yet, classic predator–prey models assume spatially homogeneous interactions between predators and prey. We developed a spatially informed theory that predicts how habitat heterogeneity alters the landscape-scale distribution of mortality risk of prey from predation, and hence the nature of predator interactions in multiprey systems. The theoretical model is a spatially explicit, multiprey functional response in which species-specific advection–diffusion models account for the response of individual prey to habitat edges. The model demonstrates that distinct responses of alternative prey species can alter the consequences of conspecific aggregation, from increasing safety to increasing predation risk. Observations of threatened boreal caribou, moose and grey wolf interacting over 378 181 km² of human-managed boreal forest support this principle. This empirically supported theory demonstrates how distinct responses of apparent competitors to landscape heterogeneity, including to human disturbances, can reverse density dependence in fitness correlates.     

Vole fluctuations,red fox responses,predation on fawns,and roe deer dynamics in a temperate latitude

The alternative prey hypothesis predicts that predators respond both functionally and numerically (with a time lag) to fluctuations in the main prey abundance, which affects the survival of alternative prey. This pattern was found in northern Europe in the community formed by voles (Microtidae), red foxes (Vulpes vulpes) and roe deer (Capreolus capreolus). We studied the same predator—prey community in a temperate latitude where, according to the predation hypothesis, only the functional response of predators to changes in main prey availability should occur. In the years 1997–2007, in western Poland, we estimated the index of common vole (Microtus arvalis) abundance (burrow counts), the density of foxes (spotlight counts), the young production in foxes (young/adult ratio), the index of fox predation on fawns (prey remains near dens) as well as the reproduction index (fawn/female ratio) and density of roe deer (total counts). The vole abundance fluctuated considerably, the young production in foxes did not correlate with the main prey availability, but the density of foxes showed direct numerical response. The index of fox predation on fawns decreased with the vole abundance and negatively affected the fawn/female ratio in roe deer. Thus, the relationships between voles and foxes were not fully consistent with the predation hypothesis. The direct numerical response of foxes should tend to stabilize this predator—prey community. It is suggested, however, that responses showed by vole-eating predators in temperate latitudes may sometimes affect their alternative prey, including animals with unfavourable conservation status.